I can't fuckin believe he backed down after Luka intervened. Who in his right mind and power crosses the Rubicon, then crosses it back? Prigozhin will lose his power AND life soon because of this dumb decision
My guess is he didn't get the reaction he expected and was offered exile. He saw a quick death if he continued and the chance to defect west or something if he stopped. I think stopping becomes the obvious move in that case.
The bigger question is why did he start in the first place? What conditions existed that meant that was the best move.
My million dollars question really is: what Luka told him to stop? My money's on something like "we have your daughter", which, as I remember, is living in St. Petersburg